Beyond \(a=c\): gravitational couplings to matter and the stress tensor OPE

DOI10.1007/JHEP07(2018)157zbMATH Open1395.83092arXiv1712.04861WikidataQ129457078 ScholiaQ129457078MaRDI QIDQ2413755

Author name not available (Why is that?)

Publication date: 14 September 2018

Published in: (Search for Journal in Brave)

Abstract: We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, $langleTTcalOangle=0$, where $calOeqT$ is a single-trace primary. We show that this follows from a suppression of $langleTTcalOangle$ by powers of the higher spin gap, $Delt{a}_{mgap}$, dual to the bulk mass scale of higher spin particles, and explain why $langleTTcalOangle$ is a more sensitive probe of $Delt{a}_{mgap}$ than $a-c$ in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings $langleT{calO}_1{calO}_{2}angle$ where ${calO}_i$ have spin $s_{i}leq2$, we are led to propose that $1/Delt{a}_{mgap}$ is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on $TT$ couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of $langleTTTangle$ in the free-field basis are nonzero in interacting CFTs.

Full work available at URL: https://arxiv.org/abs/1712.04861

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Beyond \(a=c\): gravitational couplings to matter and the stress tensor OPE

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2413755)